Exponential and Logarithmic Functions Chapter 9 Exponential and Logarithmic Functions

Chapter Sections 9.1 – Composite and Inverse Functions 9.2 – Exponential Functions 9.3 – Logarithmic Functions 9.4 – Properties of Logarithms 9.5 – Common Logarithms 9.6 – Exponential and Logarithmic Equations 9.7 – Natural Exponential and Natural Logarithmic Functions Chapter 1 Outline

Exponential Functions § 9.2 Exponential Functions

Graph Exponential Functions To Find the Inverse Function of a One-to-One Function For any real number a > 0 and a ≠ 1, is an exponential function Examples of Exponential Functions

Graph Exponential Functions Graphs of Exponential Functions For all exponential functions of the form y = ax or f(x) =ax, where a > 0 and a ≠ 1, The domain of the function is The range of the function is The graph of the function passes through the points

Graph Exponential Functions Example Graph the exponential function y = 2x. State the domain and range of the function. The function is the form y = ax, where a = 2. First construct a table of values. continued

Graph Exponential Functions Now plot these points and connect them with a smooth curve. The domain of this function is the set of all real numbers, or (-∞,∞). The range is {y|y > 0} or (0,∞).

Solve Applications of Exponential Functions Compound Interest Formula The accumulated amount, A, in a compound interest account can be found using the formula where p is the principal or the initial investment amount, r is the interest rate as a decimal, n is the number of compounding periods per year, and t is the time in years.

Solve Applications of Exponential Functions Example Nancy Johnson invests $10,000 in certificate of deposit (CD) with 5% interest compounded quarterly for 6 years. Determine the value of the CD after 6 years. The principal, p, is $10,000 and the interest rate, r, is 5%. Because the interest is compounded quarterly, the number of compounding periods, n, is 4. The money is invested for 6 years so t is 6. Substitute these values into the formula. continued

Solve Applications of Exponential Functions The original $10,000 has grown to about $13,473.51 after 6 years.